U.S. Pat. No. 7,217,453 discloses a composite laminate sandwich structure including outside skins of a polymer matrix composite, an internal core, and a Z-axis fiber reinforcement through the composite laminate and normal to the plane of the polymer matrix composite skins. The composite laminate sandwich structure disclosed in U.S. Pat. No. 7,217,453 is excellent for many applications. The inventors of the present invention, some of who are the same as the inventors of U.S. Pat. No. 7,217,453, have developed a new composite laminate sandwich structure that is ideal for applications where a higher shear modulus, greater stiffness, less deflection, and higher load-carrying capability are required.